joint cumulative distribution function

Let X1,X2,,Xn be n random variablesMathworldPlanetmath all defined on the same probability spaceMathworldPlanetmath. The joint cumulative distribution function of X1,X2,,Xn, denoted by FX1,X2,,Xn(x1,x2,,xn), is the following function:


As in the unidimensional case, this function satisfies:

  1. 1.

    lim(x1,,xn)(-,,-)FX1,X2,,Xn(x1,,xn)=0 and lim(x1,,xn)(,,)FX1,X2,,Xn(x1,,xn)=1

  2. 2.

    FX1,X2,,Xn(x1,,xn) is a monotoneMathworldPlanetmath, nondecreasing function.

  3. 3.

    FX1,X2,,Xn(x1,,xn) is continuousMathworldPlanetmath from the right in each variable.

The way to evaluate FX1,X2,,Xn(x1,,xn) is the following:


(if F is continuous) or


(if F is discrete),

where fX1,X2,,Xn is the joint density function of X1,,Xn.

Title joint cumulative distribution function
Canonical name JointCumulativeDistributionFunction
Date of creation 2013-03-22 11:54:52
Last modified on 2013-03-22 11:54:52
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 9
Author mathcam (2727)
Entry type Definition
Classification msc 60A10
Synonym joint cumulative distribution